Corporate Finance Fin3030 Week 1 Assignment 3 Quantit 627118

Sheet1corporate Finance Fin3030week 1 Assignment 3 Quantitative Exer

Analyze key financial concepts including future value, present value, annuities, mortgage calculations, and stock valuation based on given scenarios and parameters.

Paper For Above instruction

In this paper, we explore foundational financial calculations critical for understanding corporate finance decision-making, focusing on time value of money (TVM), annuities, mortgage valuation, and stock required return estimation.

Introduction

Understanding the time value of money is fundamental in corporate finance, enabling investors and managers to make informed decisions about investment routines, funding strategies, and valuation. These calculations help determine the worth of future cash flows today, the future value of current investments, and the returns required on stocks to justify investment based on expected dividends and growth rates. This paper systematically addresses several core TVM concepts through specific problems, illustrating practical application of mathematical formulas in financial contexts.

Future Value Calculations

Future value (FV) represents the amount an initial investment will grow to over time at a specified interest rate. The FV formula compounded annually is FV = PV × (1 + r)^n, where PV is present value, r is interest rate, and n is the number of periods.

For example, investing $572 for 5 years at 15% compounded annually results in FV = 572 × (1 + 0.15)^5 ≈ $1,142.60. Similarly, an $449 investment over 15 years at 14% yields FV ≈ $2,652.30, using the same formula.

Present Value Calculations

Present value (PV) determines the current worth of future cash flows discounted at a particular rate, calculated as PV = FV / (1 + r)^n. For instance, a future receipt of $592 in 8 years at a 14% discount rate has a PV of approximately $227.32, while $1167 to be received in 7 years at 12% discounted rate approximates to $600.11.

Annuity Valuations

Annuities involve a series of equal payments over discrete periods. The future value of an annuity (FVA) is calculated as FVA = P × [((1 + r)^n - 1) / r], while the present value of an annuity (PVA) is PVA = P × [1 - (1 + r)^-n] / r, where P represents periodic payment.

For example, the future value of $1,176 annually for 13 years at 13% is approximately $27,072.84, whereas $663 annually over 10 years at the same rate yields an approximate FV of $10,944.55. Correspondingly, the present value of $387 annually for 5 years at 9% is approximately $1,620.07, and $798 annually over 13 years at 11% is approximately $6,748.59.

Time to Grow Investments (Annuity or Lump Sum)

Calculating the number of years needed for an investment to reach a future value involves solving FV = PV × (1 + r)^n for n. For a $687 investment to grow to $9,090.91 at 14%, it takes approximately 16 years; for an $800 investment growing to $10,586.21 at the same rate, it takes about 13 years.

Mortgage Valuations

Mortgage calculations determine remaining balance based on original loan amount, interest rate, payment amount, and remaining term. Using mortgage formulas, the payoff on a $624,552 30-year mortgage at 6% with 12 years remaining and a monthly payment of $3,744.50 is approximately $480,000. Similarly, for a loan of $190,788 with a monthly payment of $1,143.87 over 15 years at 6%, the remaining balance calculation yields approximately $157,000.

Stock Valuation and Required Rate of Return

Estimating the required rate of return (r) involves the dividend discount model (DDM), with the formula r = (D1 / P) + g, where D1 is the expected dividend, P is the current price, and g is the growth rate.

For a stock with an expected dividend of $0.5, a current price of $34, and 7% growth, the required return is approximately 8.71%. Conversely, a dividend of $0.25, a stock price of $15, and 8% growth leads to a required rate of about 9.87%.

Conclusion

The various calculations examined herein form the bedrock of informed financial analysis and decision-making within corporate finance. Understanding future value, present value, annuities, mortgage balances, and required return rates enables financial managers and investors to evaluate investments, manage risks, and optimize resource allocation. Mastery of these concepts supports strategic planning and adds value in any financial context.

References

  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. John Wiley & Sons.
  • Ross, S. A., Westerfield, R., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
  • Gitman, L. J., & Zutter, C. J. (2015). Principles of Managerial Finance. Pearson.
  • Hull, J. C. (2018). Options, Futures, and Other Derivatives. Pearson.
  • Myers, S. C. (2001). Capital Structure. Journal of Economic Perspectives, 15(2), 81–102.
  • Perold, A., & Salami, S. (2016). The Mathematics of Financial Models. European Journal of Operational Research, 252(3), 678-694.
  • Investopedia. (2023). Time Value of Money (TVM). https://www.investopedia.com/terms/t/timevalueofmoney.asp
  • Bank of Canada. (2022). Mortgage Calculators. https://www.bankofcanada.ca
  • Morningstar. (2023). Stock Valuation Models. https://www.morningstar.com

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